Question

The following table gives the number of pages written by Sarika for completing her own book for 30 days:

Number of pages written per day	16 – 18	19 – 21	22 – 24	25 – 27	28 – 30
Number of days	1	3	4	9	13

Find the mean number of pages written per day.

Answer 1

No need to change the class-intervals into continuous intervals as Classmarks of continuous and discontinuous classes are same.

d_i is deviation from assumed mean.

Class interval	Mid Value `(bb(x_i))`	`bb(d_i = (x_i - a))`	No. of days `(bb(f_i))`	`bb(f_i d_i)`
16 – 18	17	– 6	1	– 6
19 – 21	20	– 3	3	– 9
22 – 24	a = 23	0	4	0
25 – 27	26	3	9	27
28 – 30	29	6	13	78
			`sumf_i = 30`	`sumf_i d_i = 90`

a = assumed mean, a = 23

`barx = a + (sumf_i d_i)/(sumf_i)`

= `23 + 90/30`

= 23 + 3

= 26

∴ `barx` = 26

Hence, the mean of pages written per day is 26.